Migrate release channels to use .ci.yaml

[christopherfujino]

• Stable Framework - [flutter_releases] Flutter Stable 2.2.x update .ci.yaml targets #86586
• Stable Engine - [flutter_releases] Migrate stable *_builders.json to ci.yaml engine#27486
• Beta Framework - [ci.yaml] Nest tags under properties (#86364) #86445
• Beta Engine - [flutter_release] Update beta .ci.yaml engine#27487

[CaseyHillers]

This is complete with the latest beta release

[github-actions]

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